Finite Group Databasebeta

← #35197227

Subgroups — #35197227

Order 20224.

6428 conjugacy classes of subgroups.

The subgroup lattice has 1816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778005C214yesmaximal, complemented
2#23778001C214yesmaximal, complemented
3#23777892C212yesmaximal, complemented
4#23777884C212yesmaximal, complemented
5#23777877C214yesmaximal, complemented
6#23777876C212yesmaximal, complemented
7#23777813C212yesmaximal, complemented
8#23777646C214yesmaximal, complemented
9#23777497C212yesmaximal, complemented
10#23777495C212yesmaximal, complemented
11#23777489C214yesmaximal, complemented
12#23777287C212yesmaximal, complemented
13#23777284C211yesmaximal, characteristic, complemented
14#23777279C212yesmaximal, complemented
15#23777279C212yesmaximal, complemented
16#23777264C212yesmaximal, complemented
17#23777255C212yesmaximal, complemented
18#23777219C211yesmaximal, characteristic, complemented
19#23777212C211yesmaximal, characteristic, complemented
20#23777212C212yesmaximal, complemented
21#23777206C212yesmaximal, complemented
22#23777204C212yesmaximal, complemented
23#23777149C212yesmaximal, complemented
24#23777142C212yesmaximal, complemented
25#23777141C214yesmaximal, complemented
26#23776693C211yesmaximal, characteristic
27C2×#19099118C211yesmaximal, characteristic, complemented
28#533×D79C211yesmaximal, characteristic, complemented
29C79×#3509C211yesmaximal, characteristic, complemented
30C79⋊#564C2218yescomplemented
31#19099317C2218yes—
32#19099315C2218yes—
33#19099315C2218yescomplemented
34#19099295C2214yescomplemented
35Q8×Dic158C2214yescomplemented
36Q8×Dic158C2212yescomplemented
37Q8×Dic158C2214yescomplemented
38Q8×Dic158C2212yescomplemented
39#19099292C2214yescomplemented
40#19099292C2214yescomplemented
41#19099292C2214yescomplemented
42#19099292C2212yescomplemented
43#19099291C2214yescomplemented
44#19099291C2212yescomplemented
45#19099290C2218yescomplemented
46#19099290C2214yescomplemented
47#19099290C2214yescomplemented
48#19099289C2214yescomplemented
49#19099289C2214yescomplemented
50#19099289C2214yescomplemented
51#19099289C2214yescomplemented
52#19099288C2212yescomplemented
53#19099288C2212yescomplemented
54#19099288C2214yescomplemented
55#19099287C2212yescomplemented
56#19099287C2212yescomplemented
57#19099287C2214yescomplemented
58#19099286C2214yes—
59#19099286C2214yes—
60#19099284C2214yes—
61#19099284C2214yescomplemented
62#19099282C2214yescomplemented
63#19099281C2214yes—
64#19099281C2214yescomplemented
65#19099280C2218yescomplemented
66#19099273C2214yes—
67#19099273C2212yescomplemented
68#19099271C2214yes—
69#19099271C2214yes—
70#19099271C2214yescomplemented
71#19099270C2214yes—
72#19099270C2212yescomplemented
73#19099255C2214yes—
74#19099255C2214yes—
75#19099255C2214yescomplemented
76#19099255C2214yescomplemented
77#19099254C2214yes—
78#19099254C2214yes—
79#19099252C2214yes—
80#19099252C2214yescomplemented
81#19099251C2214yes—
82#19099251C2214yes—
83#19099251C2218yes—
84#19099250C2218yes—
85#19099249C2218yes—
86#19099248C2214yes—
87#19099248C2214yes—
88#19099247C2214yes—
89#19099247C2214yescomplemented
90#19099246C2218yes—
91#19099237C2218yes—
92#19099236C2218yes—
93Q8×D316C2214yes—
94Q8×D316C2212yescomplemented
95D4×Dic158C2214yes—
96D4×Dic158C2212yescomplemented
97#19099226C2214yes—
98#19099226C2214yes—
99#19099226C2214yescomplemented
100#19099193C2218yes—
101#19099193C2214yes—
102#19099193C2214yescomplemented
103#19099193C2214yescomplemented
104#19099191C2218yes—
105#19099191C2212yes—
106#19099191C2212yes—
107#19099191C2214yescomplemented
108#19099191C2214yescomplemented
109#19099185C2214yes—
110#19099182C2214yes—
111#19099179C2218yes—
112#19099176C2214yes—
113#19099176C2214yescomplemented
114#19099176C2218yescomplemented
115#19099174C2214yes—
116#19099174C2214yescomplemented
117#19099173C2214yescomplemented
118#19099173C2214yescomplemented
119#19099172C2218yes—
120#19099172C2218yescomplemented
121#19099171C2214yes—
122#19099171C2214yes—
123#19099171C2214yescomplemented
124#19099170C2218yescomplemented
125#19099170C2218yescomplemented
126#19099157C2218yes—
127#19099154C2218yes—
128#19099139C2214yes—
129#19099137C2212yes—
130#19099136C2214yes—
131#19099136C2214yes—
132#19099120C2211yescharacteristic
133#19099120C2212yescomplemented
134#19099119C2212yes—
135#19099118C2211yescharacteristic
136#19099118C2212yes—
137#19099118C2212yes—
138#19099118C2212yes—
139#19099118C2212yes—
140#19099118C2214yes—
141#19099118C2211yescharacteristic
142#19099118C2212yes—
143#19099118C2212yes—
144#19099118C2212yes—
145#19099118C2212yes—
146#19099118C2212yescomplemented
147#19099118C2212yescomplemented
148#19099118C2212yescomplemented
149#19099117C2212yes—
150#19099117C2212yes—
151#19099117C2211yescharacteristic
152#19099117C2214yes—
153#19099117C2211yescharacteristic
154#19099116C2218yes—
155#19099116C2212yes—
156#19099116C2211yescharacteristic
157#19099115C2212yes—
158#19099115C2212yes—
159#19099110C2211yescharacteristic
160#19099110C2211yescharacteristic
161#19099109C2211yescharacteristic
162C2×#14579161C2211yescharacteristic
163C2×#14579161C2212yescomplemented
164C4⋊Q8×D79C2211yescharacteristic
165C4⋊Q8×D79C2211yescharacteristic
166C4⋊Q8×D79C2212yescomplemented
167#19099100C2211yescharacteristic
168#19099100C2214yes—
169#19099100C2211yescharacteristic
170#19099095C2211yescharacteristic
171#19099095C2211yescharacteristic
172#19099093C2212yes—
173#19099093C2212yes—
174#19099092C2214yes—
175#19099091C2212yes—
176#19099091C2212yes—
177#19099090C2218yes—
178C2×#14579152C2212yes—
179#125×D79C2212yes—
180#19099075C2211yescharacteristic
181#19099072C2212yes—
182#19099072C2212yes—
183#19099070C2211yescharacteristic
184C2×#14579141C2212yes—
185C2×#14579137C2212yes—
186C22⋊Q8×D79C2212yes—
187C22⋊Q8×D79C2212yes—
188#19099046C2212yes—
189#19099043C2214yes—
190#19099043C2212yes—
191#19099041C2212yes—
192#19099040C2214yescomplemented
193#19099039C2214yes—
194#19099039C2214yescomplemented
195C4×#11929624C2211yescharacteristic
196C4×#11929624C2212yes—
197C4×#11929624C2212yes—
198C2×Q8×Dic79C2212yes—
199C2×#14579126C2212yes—
200C4×Q8×D79C2212yes—
201C4×Q8×D79C2212yes—
202C2×#14579119C2212yes—
203#117×D79C2212yes—
204C2×C42×D79C2211yescharacteristic
205#557×C79C2212yescomplemented
206#557×C79C2212yescomplemented
207#556×C79C2212yescomplemented
208#556×C79C2212yescomplemented
209#552×C79C2214yes—
210#552×C79C2214yes—
211#541×C79C2214yescomplemented
212#536×C79C2212yes—
213#533×C79C2211yescharacteristic
214#533×C79C2212yescomplemented
215#533×C79C2212yescomplemented
216C2×C4⋊Q8×C79C2211yescharacteristic
217#519×C79C2212yes—
218C4×#41×C79C2211yescharacteristic
219C2×#11929624C2312yes—
220C2×#11929624C2311yescharacteristic
221C2×#11929624C2312yes—
222C22×Dic158C2314yes—
223C22×Dic158C2312yes—
224C2×Q8×D79C2312yes—
225C2×Q8×D79C2314yes—
226C2×Q8×D79C2312yes—
227C22×C4×D79C2311yescharacteristic
228C22×C4×D79C2311yescharacteristic
229C22×C4×D79C2311yescharacteristic
230#14579161C2318yes—
231#14579161C2314yes—
232#14579161C2318yes—
233#14579161C2314yes—
234#14579161C2314yes—
235#14579161C2312yes—
236#14579161C2314yes—
237#14579161C2312yes—
238#14579161C2312yes—
239#14579161C2311yescharacteristic
240#14579161C2311yescharacteristic
241#14579161C2312yes—
242#14579160C2318yes—
243#14579160C2318yes—
244#14579160C2318yes—
245#14579160C2318yes—
246#14579160C2318yes—
247#14579160C2318yes—
248#14579160C2314yes—
249#14579160C2314yes—
250#14579160C2312yes—
251#14579160C2314yes—
252#14579160C2312yes—
253#14579160C2312yes—
254#14579160C2312yes—
255#14579160C2311yescharacteristic
256#14579160C2311yescharacteristic
257#14579159C2314yes—
258#14579159C2314yes—
259#14579159C2312yes—
260#14579159C2312yes—
261#14579159C2311yescharacteristic
262#14579157C2311yescharacteristic
263#14579156C2318yes—
264#14579156C2318yes—
265#14579156C2318yes—
266#14579156C2318yes—
267#14579156C2318yes—
268#14579156C2312yes—
269#14579156C2318yes—
270#14579156C2318yes—
271#14579156C2312yes—
272#14579156C2318yes—
273#14579155C2318yes—
274#14579155C2318yes—
275#14579154C2318yes—
276#14579154C2312yes—
277#14579154C2312yes—
278#14579154C2318yes—
279#14579154C2318yes—
280#14579154C2318yes—
281#14579153C2318yes—
282#14579153C2318yes—
283#14579153C2318yes—
284#14579153C2314yes—
285#14579153C2312yes—
286#14579153C2314yes—
287#14579152C2318yes—
288#14579152C2318yes—
289#14579152C2314yes—
290#14579152C2318yes—
291#14579152C2314yes—
292#14579152C2314yes—
293#14579152C2314yes—
294#14579152C2318yes—
295#14579152C2318yes—
296#14579152C2318yes—
297#14579152C2318yes—
298#14579152C2314yes—
299#14579152C2314yes—
300#14579152C2312yes—
301#14579152C2314yes—
302#14579152C2312yes—
303#14579152C2311yescharacteristic
304#14579152C2311yescharacteristic
305#14579152C2314yes—
306#14579151C2318yes—
307#14579151C2314yes—
308#14579151C2318yes—
309#14579151C2318yes—
310#14579151C2318yes—
311#14579151C2318yes—
312#14579151C2318yes—
313#14579151C2318yes—
314#14579151C2318yes—
315#14579151C2318yes—
316#14579151C2312yes—
317#14579151C2314yes—
318#14579151C2312yes—
319#14579150C2314yes—
320#14579150C2311yescharacteristic
321#14579149C2318yes—
322#14579148C2311yescharacteristic
323#14579147C2318yes—
324#14579147C2318yes—
325#14579147C2312yes—
326#14579147C2312yes—
327#14579146C2318yes—
328#14579146C2318yes—
329#14579146C2312yes—
330#14579146C2312yes—
331#14579145C2318yes—
332#14579145C2318yes—
333#14579145C2312yes—
334#14579144C2318yes—
335#14579143C2318yes—
336#14579143C2318yes—
337#14579143C2312yes—
338#14579143C2312yes—
339#14579142C2312yes—
340#14579141C2314yes—
341#14579141C2314yes—
342#14579141C2312yes—
343#14579141C2314yes—
344#14579141C2314yes—
345#14579141C2314yes—
346#14579141C2318yes—
347#14579141C2311yescharacteristic
348#14579141C2318yes—
349#14579141C2318yes—
350#14579141C2314yes—
351#14579141C2312yes—
352#14579141C2314yes—
353#14579141C2311yescharacteristic
354#14579140C2314yes—
355#14579140C2314yes—
356#14579140C2312yes—
357#14579140C2312yes—
358#14579139C2318yes—
359#14579139C2312yes—
360#14579139C2314yes—
361#14579139C2318yes—
362#14579139C2312yes—
363#14579139C2318yes—
364#14579139C2314yes—
365#14579138C2318yes—
366#14579138C2314yes—
367#14579138C2318yes—
368#14579138C2318yes—
369#14579138C2318yes—
370#14579138C2312yes—
371#14579138C2318yes—
372#14579138C2318yes—
373#14579138C2314yes—
374#14579138C2312yes—
375#14579137C2312yes—
376#14579137C2314yes—
377#14579137C2314yes—
378#14579137C2314yes—
379#14579137C2314yes—
380#14579137C2311yescharacteristic
381#14579137C2314yes—
382#14579137C2314yes—
383#14579137C2312yes—
384#14579137C2314yes—
385#14579137C2311yescharacteristic
386#14579136C2311yescharacteristic
387#14579136C2311yescharacteristic
388#14579134C2312yes—
389#14579134C2312yes—
390#14579133C2312yes—
391#14579133C2312yes—
392#14579132C2311yescharacteristic
393#14579132C2311yescharacteristic
394#14579131C2312yes—
395#14579129C2312yes—
396Q8×Dic79C2312yes—
397Q8×Dic79C2314yes—
398Q8×Dic79C2314yes—
399Q8×Dic79C2314yes—
400Q8×Dic79C2314yes—
401Q8×Dic79C2314yes—
402Q8×Dic79C2314yes—
403Q8×Dic79C2314yes—
404Q8×Dic79C2312yes—
405Q8×Dic79C2314yes—
406Q8×Dic79C2314yes—
407Q8×Dic79C2314yes—
408C4×Dic158C2318yes—
409C4×Dic158C2318yes—
410C4×Dic158C2314yes—
411C4×Dic158C2314yes—
412C4×Dic158C2314yes—
413C4×Dic158C2318yes—
414C4×Dic158C2318yes—
415C4×Dic158C2318yes—
416C4×Dic158C2312yes—
417C4×Dic158C2312yes—
418C4×Dic158C2314yes—
419C4×Dic158C2314yes—
420C4×Dic158C2311yescharacteristic
421C4×Dic158C2311yescharacteristic
422C4×Dic158C2312yes—
423C4×Dic158C2312yes—
424C4×Dic158C2312yes—
425C4×Dic158C2312yes—
426#14579126C2314yes—
427#14579126C2314yes—
428#14579126C2318yes—
429#14579126C2314yes—
430#14579126C2314yes—
431#14579126C2314yes—
432#14579126C2314yes—
433#14579126C2312yes—
434#14579126C2318yes—
435#14579126C2314yes—
436#14579126C2312yes—
437#14579126C2314yes—
438#14579126C2314yes—
439C4×D316C2318yes—
440C4×D316C2314yes—
441C4×D316C2312yes—
442C4×D316C2311yescharacteristic
443C4×D316C2312yes—
444C4×D316C2312yes—
445C4×D316C2312yes—
446C4×D316C2311yescharacteristic
447D4×Dic79C2318yes—
448D4×Dic79C2314yes—
449C4×C22⋊D79C2312yes—
450C4×C22⋊D79C2312yes—
451C4×C22⋊D79C2312yes—
452C4×C22⋊D79C2312yes—
453C4×C22⋊D79C2312yes—
454C4×C22⋊D79C2312yes—
455C4×C22⋊D79C2312yes—
456C4×C22⋊D79C2312yes—
457C4×C22⋊D79C2312yes—
458C4×C22⋊D79C2312yes—
459(C22⋊D79)⋊C4C2318yes—
460(C22⋊D79)⋊C4C2318yes—
461(C22⋊D79)⋊C4C2318yes—
462#14579120C2312yes—
463#14579120C2312yes—
464#14579120C2312yes—
465#14579120C2311yescharacteristic
466#14579120C2318yes—
467#14579120C2314yes—
468#14579119C2314yes—
469#14579119C2314yes—
470#14579119C2314yes—
471#14579119C2318yes—
472#14579119C2318yes—
473#14579119C2314yes—
474#14579119C2314yes—
475#14579119C2314yes—
476#14579119C2314yes—
477#14579119C2312yes—
478#14579119C2312yes—
479#14579118C2312yes—
480#14579118C2314yes—
481#14579118C2312yes—
482#14579118C2312yes—
483#14579118C2312yes—
484#14579118C2318yes—
485#14579118C2312yes—
486#14579118C2318yes—
487#14579117C2318yes—
488#14579117C2318yes—
489#14579117C2314yes—
490C2×C4⋊Dic79C2314yes—
491C2×C4⋊Dic79C2312yes—
492C2×C4⋊Dic79C2314yes—
493C2×C4⋊Dic79C2314yes—
494C2×C4⋊Dic79C2312yes—
495C2×Dic79⋊C4C2314yes—
496C4⋊C4×D79C2314yes—
497C4⋊C4×D79C2312yes—
498C4⋊C4×D79C2314yes—
499C4⋊C4×D79C2314yes—
500C4⋊C4×D79C2312yes—
501C4⋊C4×D79C2314yes—
502C4⋊C4×D79C2312yes—
503C4⋊C4×D79C2312yes—
504C2×(C2×D79)⋊C4C2314yes—
505C22⋊C4×D79C2314yes—
506C2×C4×Dic79C2311yescharacteristic
507C2×C4×Dic79C2311yescharacteristic
508C2×C4×Dic79C2311yescharacteristic
509C2×C4×Dic79C2314yes—
510C42×D79C2311yescharacteristic
511C42×D79C2311yescharacteristic
512C42×D79C2311yescharacteristic
513C42×D79C2311yescharacteristic
514C42×D79C2311yescharacteristic
515C42×D79C2311yescharacteristic
516C42×D79C2311yescharacteristic
517C42×D79C2311yescharacteristic
518C42×D79C2314yes—
519C42×D79C2312yes—
520C2×#41×C79C2311yescharacteristic
521C22×Q8×C79C2312yes—
522C4⋊Q8×C79C2314yes—
523C4⋊Q8×C79C2312yes—
524C4⋊Q8×C79C2312yes—
525C4⋊Q8×C79C2312yes—
526C4⋊Q8×C79C2312yes—
527C4⋊Q8×C79C2311yescharacteristic
528C4⋊Q8×C79C2311yescharacteristic
529#126×C79C2318yes—
530#126×C79C2318yes—
531#125×C79C2318yes—
532#125×C79C2318yes—
533#125×C79C2314yes—
534#125×C79C2314yes—
535#125×C79C2312yes—
536#124×C79C2314yes—
537#123×C79C2318yes—
538C22⋊Q8×C79C2314yes—
539C22⋊Q8×C79C2314yes—
540C22⋊Q8×C79C2312yes—
541C22⋊Q8×C79C2314yes—
542C22⋊Q8×C79C2314yes—
543C22⋊Q8×C79C2312yes—
544C4×Q8×C79C2314yes—
545C4×Q8×C79C2314yes—
546C4×Q8×C79C2314yes—
547C4×Q8×C79C2314yes—
548C4×Q8×C79C2312yes—
549C4×Q8×C79C2311yescharacteristic
550C4×Q8×C79C2311yescharacteristic
551C4×Q8×C79C2314yes—
552C4×Q8×C79C2314yes—
553C4×Q8×C79C2312yes—
554C4×D4×C79C2312yes—
555C4×D4×C79C2311yescharacteristic
556C4×D4×C79C2312yes—
557C4×D4×C79C2311yescharacteristic
558#117×C79C2314yes—
559#117×C79C2311yescharacteristic
560#117×C79C2318yes—
561#117×C79C2312yes—
562#117×C79C2312yes—
563#117×C79C2314yes—
564C2×C4⋊C4×C79C2312yes—
565C2×C4⋊C4×C79C2312yes—
566C2×C42×C79C2311yescharacteristic
567C2×C42×C79C2312yes—
568C23×D79C2411yescharacteristic
569#11929624—28no—
570#11929624—24no—
571#11929624—44no—
572C2×Dic158—44no—
573C2×Dic158—48no—
574C2×Dic158C2414yes—
575C2×Dic158C2412yes—
576C2×Dic158C2414yes—
577C2×Dic158C2412yes—
578C2×Dic158C2412yes—
579C2×Dic158C2411yescharacteristic
580C2×Dic158C2414yes—
581C2×Dic158C2418yes—
582C2×Dic158C2414yes—
583C2×Dic158C2418yes—
584C2×Dic158C2412yes—
585Q8×D79—28no—
586Q8×D79—44no—
587Q8×D79—48no—
588C2×D316C2412yes—
589C2×D316C2411yescharacteristic
590C2×D316C2412yes—
591C2×C22⋊D79C2412yes—
592C2×C22⋊D79C2412yes—
593C2×C22⋊D79C2412yes—
594C2×C22⋊D79C2412yes—
595C2×C22⋊D79C2412yes—
596C22×Dic79C2411yescharacteristic
597C22×Dic79C2411yescharacteristic
598C22×Dic79C2414yes—
599C22×Dic79C2418yes—
600C22×Dic79C2411yescharacteristic
601C2×C4×D79—24no—
602C2×C4×D79—24no—
603C2×C4×D79—42no—
604C2×C4×D79C2412yes—
605C2×C4×D79C2411yescharacteristic
606C2×C4×D79C2414yes—
607C2×C4×D79C2411yescharacteristic
608C2×C4×D79C2412yes—
609C2×C4×D79C2412yes—
610C2×C4×D79C2411yescharacteristic
611C2×C4×D79C2411yescharacteristic
612C2×C4×D79C2411yescharacteristic
613C2×C4×D79C2411yescharacteristic
614C2×C4×D79C2411yescharacteristic
615C2×C4×D79C2411yescharacteristic
616C2×C4×D79C2411yescharacteristic
617C2×C4×D79C2414yes—
618C2×C4×D79C2418yes—
619C2×C4×D79C2411yescharacteristic
620C2×C4×D79C2411yescharacteristic
621C2×C4×D79C2411yescharacteristic
622C4⋊Dic79C2412yes—
623C4⋊Dic79C2414yes—
624C4⋊Dic79C2414yes—
625C4⋊Dic79C2412yes—
626C4⋊Dic79C2412yes—
627C4⋊Dic79C2414yes—
628C4⋊Dic79C2412yes—
629C4⋊Dic79C2414yes—
630C4⋊Dic79C2414yes—
631C4⋊Dic79C2414yes—
632C4⋊Dic79C2418yes—
633C4⋊Dic79C2418yes—
634C4⋊Dic79C2418yes—
635C4⋊Dic79C2418yes—
636C4⋊Dic79C2418yes—
637C4⋊Dic79C2412yes—
638C4⋊Dic79C2412yes—
639C4⋊Dic79C2411yescharacteristic
640C4⋊Dic79C2411yescharacteristic
641C4⋊Dic79C2412yes—
642C4⋊Dic79C2412yes—
643C4⋊Dic79C2418yes—
644C4⋊Dic79C2418yes—
645Dic79⋊C4C2414yes—
646Dic79⋊C4C2414yes—
647Dic79⋊C4C2414yes—
648Dic79⋊C4C2414yes—
649Dic79⋊C4C2418yes—
650Dic79⋊C4C2418yes—
651Dic79⋊C4C2414yes—
652Dic79⋊C4C2414yes—
653Dic79⋊C4C2414yes—
654Dic79⋊C4C2414yes—
655Dic79⋊C4C2418yes—
656Dic79⋊C4C2418yes—
657Dic79⋊C4C2418yes—
658Dic79⋊C4C2418yes—
659Dic79⋊C4C2412yes—
660Dic79⋊C4C2412yes—
661Dic79⋊C4C2412yes—
662Dic79⋊C4C2412yes—
663Dic79⋊C4C2412yes—
664Dic79⋊C4C2412yes—
665Dic79⋊C4C2412yes—
666Dic79⋊C4C2412yes—
667Dic79⋊C4C2412yes—
668Dic79⋊C4C2412yes—
669Dic79⋊C4C2418yes—
670Dic79⋊C4C2418yes—
671Dic79⋊C4C2418yes—
672C22⋊Dic79C2414yes—
673C22⋊Dic79C2412yes—
674C22⋊Dic79C2412yes—
675C22⋊Dic79C2412yes—
676C22⋊Dic79C2412yes—
677C22⋊Dic79C2412yes—
678C22⋊Dic79C2418yes—
679(C2×D79)⋊C4C2414yes—
680(C2×D79)⋊C4C2414yes—
681(C2×D79)⋊C4C2418yes—
682(C2×D79)⋊C4C2418yes—
683(C2×D79)⋊C4C2412yes—
684(C2×D79)⋊C4C2412yes—
685(C2×D79)⋊C4C2412yes—
686(C2×D79)⋊C4C2412yes—
687(C2×D79)⋊C4C2418yes—
688(C2×D79)⋊C4C2412yes—
689(C2×D79)⋊C4C2412yes—
690(C2×D79)⋊C4C2412yes—
691(C2×D79)⋊C4C2412yes—
692(C2×D79)⋊C4C2412yes—
693(C2×D79)⋊C4C2412yes—
694(C2×D79)⋊C4C2418yes—
695(C2×D79)⋊C4C2418yes—
696C4×Dic79C2411yescharacteristic
697C4×Dic79C2411yescharacteristic
698C4×Dic79C2411yescharacteristic
699C4×Dic79C2411yescharacteristic
700C4×Dic79C2411yescharacteristic
701C4×Dic79C2411yescharacteristic
702C4×Dic79C2411yescharacteristic
703C4×Dic79C2411yescharacteristic
704C4×Dic79C2411yescharacteristic
705C4×Dic79C2411yescharacteristic
706C4×Dic79C2411yescharacteristic
707C4×Dic79C2411yescharacteristic
708C4×Dic79C2414yes—
709C4×Dic79C2414yes—
710C4×Dic79C2412yes—
711C4×Dic79C2412yes—
712C4×Dic79C2412yes—
713C4×Dic79C2414yes—
714C4×Dic79C2418yes—
715C4×Dic79C2418yes—
716C4×Dic79C2418yes—
717C4×Dic79C2418yes—
718C4×Dic79C2418yes—
719C4×Dic79C2418yes—
720#41×C79—24no—
721C2×Q8×C79—28no—
722C2×Q8×C79C2412yes—
723C2×Q8×C79C2412yes—
724C2×Q8×C79C2414yes—
725C2×Q8×C79C2414yes—
726C2×Q8×C79C2411yescharacteristic
727C2×D4×C79C2412yes—
728C2×D4×C79C2411yescharacteristic
729C22×C4×C79C2412yes—
730C22×C4×C79C2411yescharacteristic
731C22×C4×C79C2412yes—
732C22×C4×C79C2411yescharacteristic
733C22×C4×C79C2412yes—
734C22×C4×C79C2414yes—
735C22×C4×C79C2411yescharacteristic
736C4⋊C4×C79C2414yes—
737C4⋊C4×C79C2414yes—
738C4⋊C4×C79C2414yes—
739C4⋊C4×C79C2414yes—
740C4⋊C4×C79C2412yes—
741C4⋊C4×C79C2412yes—
742C4⋊C4×C79C2411yescharacteristic
743C4⋊C4×C79C2411yescharacteristic
744C4⋊C4×C79C2412yes—
745C4⋊C4×C79C2412yes—
746C4⋊C4×C79C2412yes—
747C4⋊C4×C79C2412yes—
748C4⋊C4×C79C2418yes—
749C4⋊C4×C79C2418yes—
750C4⋊C4×C79C2418yes—
751C4⋊C4×C79C2418yes—
752C4⋊C4×C79C2414yes—
753C4⋊C4×C79C2414yes—
754C22⋊C4×C79C2412yes—
755C22⋊C4×C79C2414yes—
756C22⋊C4×C79C2412yes—
757C22⋊C4×C79C2412yes—
758C22⋊C4×C79C2418yes—
759C22⋊C4×C79C2418yes—
760C42×C79C2411yescharacteristic
761C42×C79C2412yes—
762C42×C79C2411yescharacteristic
763C42×C79C2412yes—
764C42×C79C2412yes—
765C42×C79C2411yescharacteristic
766C42×C79C2411yescharacteristic
767C42×C79C2418yes—
768C42×C79C2418yes—
769C42×C79C2414yes—
770C23×C79C2512yes—
771C23×C79C2511yescharacteristic
772C22×D79—22no—
773C22×D79—22no—
774C22×D79—41no—
775C22×D79C2511yescharacteristic
776C22×D79C2512yes—
777C22×D79C2511yescharacteristic
778Q8×C79—24no—
779Q8×C79—28no—
780Q8×C79—28no—
781Q8×C79—22no—
782Q8×C79—24no—
783D4×C79—24no—
784D4×C79—22no—
785C2×C4×C79—28no—
786C2×C4×C79—22no—
787C2×C4×C79—24no—
788C2×C4×C79—24no—
789C2×C4×C79—22no—
790C2×C4×C79—24no—
791C2×C4×C792−1+414yes—
792C2×C4×C79C2518yes—
793C2×C4×C79C2512yes—
794C2×C4×C79C2514yes—
795C2×C4×C79C2511yescharacteristic
796C2×C4×C79C2511yescharacteristic
797C2×C4×C79C2514yes—
798C2×C4×C79C2512yes—
799C2×C4×C79C2512yes—
800C2×C4×C79C2511yescharacteristic
801C2×C4×C79C2511yescharacteristic
802C2×C4×C79C2511yescharacteristic
803C2×C4×C79C2511yescharacteristic
804C22⋊D79—24no—
805C22⋊D79—24no—
806C22⋊D79—24no—
807C22⋊D79—42no—
808C22⋊D79—42no—
809C2×Dic79—22no—
810C2×Dic79—22no—
811C2×Dic79—41no—
812C2×Dic79—44no—
813C2×Dic79—48no—
814C2×Dic79C2511yescharacteristic
815C2×Dic79C2511yescharacteristic
816C2×Dic79C2514yes—
817C2×Dic79C2512yes—
818C2×Dic79C2512yes—
819C2×Dic79C2512yes—
820C2×Dic79C2514yes—
821C2×Dic79C2518yes—
822C2×Dic79C2511yescharacteristic
823C2×Dic79C2511yescharacteristic
824C2×Dic79C2511yescharacteristic
825C2×Dic79C2511yescharacteristic
826D316—24no—
827D316—22no—
828D316—42no—
829C4×D79—22no—
830C4×D79—28no—
831C4×D79—22no—
832C4×D79—22no—
833C4×D79—22no—
834C4×D79—22no—
835C4×D79—22no—
836C4×D79—24no—
837C4×D79—24no—
838C4×D79—22no—
839C4×D79—22no—
840C4×D79—24no—
841C4×D79—22no—
842C4×D79—41no—
843C4×D79—41no—
844C4×D79—44no—
845C4×D79—48no—
846C4×D792−1+414yes—
847Dic158—24no—
848Dic158—22no—
849Dic158—24no—
850Dic158—28no—
851Dic158—28no—
852Dic158—24no—
853Dic158—48no—
854Dic158—44no—
855Dic158—48no—
856Dic158—44no—
857Dic158—42no—
858C22×C79—21no—
859C22×C79—21no—
860C22×C79—22no—
861C22×C79—22no—
862C22×C79—22no—
863C22×C79C2×2−1+412yes—
864C22×C79C2611yescharacteristic
865C2×D79—21no—
866C2×D79—21no—
867C2×D79—22no—
868C2×D79—22no—
869C2×D79—21no—
870C2×D79—21no—
871C2×D79—21no—
872C2×D79—22no—
873C2×D79—44no—
874C2×D79C2×2−1+412yes—
875C4×C79—22no—
876C4×C79—28no—
877C4×C79—22no—
878C4×C79—21no—
879C4×C79—24no—
880C4×C79—22no—
881C4×C79—21no—
882C4×C79—24no—
883C4×C79C2×2−1+412yes—
884C4×C79C2×2−1+412yes—
885C4×C79C2×2−1+412yes—
886C4×C79#58512yes—
887Dic79—22no—
888Dic79—22no—
889Dic79—24no—
890Dic79—21no—
891Dic79—21no—
892Dic79—21no—
893Dic79—21no—
894Dic79—22no—
895Dic79—28no—
896Dic79—24no—
897Dic79—21no—
898Dic79C2×2−1+412yes—
899#62837—791nomaximal, Sylow
900C2×C79—22no—
901C2×C79—42no—
902C2×C79C22×2−1+411yescharacteristic
903C2×C79C22×2−1+411yescharacteristic
904C2×C79C2×#58511yescharacteristic
905D79—22no—
906D79—42no—
907D79—41no—
908#3563—794no—
909#3563—794no—
910#3556—792no—
911#3555—792no—
912#3555—792no—
913#3555—794no—
914#3550—792no—
915#3538—794no—
916#3523—792no—
917#3523—792no—
918#3523—794no—
919#3509—792no—
920#3509—792no—
921#3509—792no—
922#3509—791no—
923#3509D7911yescharacteristic, complemented
924#3507—792no—
925#3507—792no—
926#3503—791no—
927#3503—792no—
928#3503—791no—
929#3502—792no—
930#3502—792no—
931#3495—794no—
932#3495—792no—
933#3495—792no—
934#3444—791no—
935C2×#533—791no—
936C2×#533—791no—
937C79#6283711yescharacteristic, complemented, Sylow
938#564—798no—
939#563—798no—
940#563—798no—
941#563—798no—
942#559—794no—
943Q82—794no—
944Q82—794no—
945Q82—792no—
946Q82—792no—
947#557—794no—
948#557—792no—
949#557—792no—
950#557—794no—
951#557—798no—
952#557—794no—
953#557—794no—
954#557—794no—
955#557—794no—
956#557—794no—
957#557—794no—
958#557—792no—
959#557—794no—
960#557—794no—
961#557—794no—
962#557—792no—
963#557C2×D7912yescomplemented
964#557C2×D7912yescomplemented
965#556—792no—
966#556—794no—
967#556—792no—
968#556—798no—
969#556—794no—
970#556—794no—
971#556—794no—
972#556—794no—
973#556—794no—
974#556—794no—
975#556—794no—
976#556C2×D7912yescomplemented
977#556C2×D7912yescomplemented
978#554—794no—
979#554—794no—
980#554—794no—
981#554—794no—
982#554—792no—
983#554—794no—
984#554—792no—
985#552—798no—
986#552—794no—
987#552—798no—
988#552—794no—
989#552—798no—
990#552—794no—
991#552—794no—
992#552—794no—
993#552—794no—
994#552—794no—
995#552—794no—
996#552—794no—
997#552—794no—
998#552—798no—
999#552—794no—
1000#552—794no—
1001#552—794no—
1002#552—794no—
1003#552C2×D7914yes—
1004#552C2×D7914yes—
1005#551—798no—
1006#551—798no—
1007D4×Q8—794no—
1008D4×Q8—794no—
1009D4×Q8—794no—
1010D4×Q8—794no—
1011D4×Q8—792no—
1012D4×Q8—794no—
1013D4×Q8—792no—
1014#544—794no—
1015#544—798no—
1016#544—794no—
1017#544—794no—
1018#544—792no—
1019#544—792no—
1020#544—798no—
1021#544—794no—
1022#544—794no—
1023#542—798no—
1024#542—794no—
1025#542—794no—
1026#541—794no—
1027#541—794no—
1028#541—798no—
1029#541—798no—
1030#541—798no—
1031#541—798no—
1032#541—794no—
1033#541—794no—
1034#541—798no—
1035#541—794no—
1036#541—794no—
1037#541—794no—
1038#541—794no—
1039#541—794no—
1040#541C2×D7914yescomplemented
1041#539—798no—
1042#539—798no—
1043#536—792no—
1044#536—794no—
1045#536—794no—
1046#536—794no—
1047#536C2×D7912yes—
1048#533—792no—
1049#533—792no—
1050#533—791no—
1051#533—791no—
1052#533—792no—
1053#533—792no—
1054#533—792no—
1055#533—792no—
1056#533—792no—
1057#533—792no—
1058#533—794no—
1059#533—792no—
1060#533—792no—
1061#533—792no—
1062#533—792no—
1063#533—792no—
1064#533—792no—
1065#533—792no—
1066#533—792no—
1067#533—791no—
1068#533—791no—
1069#533—794no—
1070#533—792no—
1071#533—791no—
1072#533—798no—
1073#533—791no—
1074#533—792no—
1075#533C2×D7911yescharacteristic
1076#533C2×D7912yescomplemented
1077#533C2×D7912yescomplemented
1078#532—791no—
1079#532—791no—
1080#532—791no—
1081C2×C4⋊Q8—791no—
1082C2×C4⋊Q8—791no—
1083C2×C4⋊Q8—792no—
1084C2×C4⋊Q8—791no—
1085C2×C4⋊Q8—792no—
1086C2×C4⋊Q8C2×D7911yescharacteristic
1087#529—794no—
1088#529—798no—
1089#529—791no—
1090#529—791no—
1091#529—794no—
1092#529—792no—
1093#529—791no—
1094#529—792no—
1095#529—791no—
1096#529—792no—
1097#529—792no—
1098C2×#125—792no—
1099C2×#125—792no—
1100#525—791no—
1101#525—792no—
1102#525—792no—
1103#525—791no—
1104C2×C22⋊Q8—792no—
1105C2×C22⋊Q8—792no—
1106C2×C22⋊Q8—792no—
1107C2×C22⋊Q8—792no—
1108#520—792no—
1109#520—792no—
1110#520—794no—
1111#519—792no—
1112#519—794no—
1113#519—794no—
1114#519—794no—
1115#519C2×D7912yes—
1116C4×#41—791no—
1117C4×#41—792no—
1118C4×#41—792no—
1119C4×#41C2×D7911yescharacteristic
1120C2×C4×Q8—792no—
1121C2×C4×Q8—792no—
1122C2×C4×Q8—792no—
1123C2×C4×Q8—792no—
1124C2×#117—792no—
1125C2×#117—792no—
1126C22×C42—791no—
1127C2×#41—792no—
1128C2×#41—792no—
1129C2×#41—791no—
1130C2×#41C22×D7911yescharacteristic
1131C22×Q8—792no—
1132C22×Q8—794no—
1133C22×Q8—792no—
1134C22×Q8—792no—
1135C22×Q8—794no—
1136C22×Q8C22×D7912yes—
1137C23×C4—791no—
1138C23×C4—791no—
1139C23×C4—791no—
1140C4⋊Q8—792no—
1141C4⋊Q8—792no—
1142C4⋊Q8—794no—
1143C4⋊Q8—791no—
1144C4⋊Q8—794no—
1145C4⋊Q8—792no—
1146C4⋊Q8—792no—
1147C4⋊Q8—792no—
1148C4⋊Q8—792no—
1149C4⋊Q8—794no—
1150C4⋊Q8—794no—
1151C4⋊Q8—791no—
1152C4⋊Q8—791no—
1153C4⋊Q8—798no—
1154C4⋊Q8—798no—
1155C4⋊Q8—794no—
1156C4⋊Q8—798no—
1157C4⋊Q8—798no—
1158C4⋊Q8—798no—
1159C4⋊Q8—798no—
1160C4⋊Q8—791no—
1161C4⋊Q8—792no—
1162C4⋊Q8—791no—
1163C4⋊Q8—792no—
1164C4⋊Q8—792no—
1165C4⋊Q8—792no—
1166C4⋊Q8—794no—
1167C4⋊Q8—794no—
1168C4⋊Q8—794no—
1169C4⋊Q8—794no—
1170C4⋊Q8—798no—
1171C4⋊Q8—798no—
1172C4⋊Q8C22×D7911yescharacteristic
1173C4⋊Q8C22×D7911yescharacteristic
1174C4⋊Q8C22×D7912yes—
1175C4⋊Q8C22×D7912yes—
1176C4⋊Q8C22×D7912yes—
1177C4⋊Q8C22×D7912yes—
1178C4⋊Q8C22×D7914yes—
1179#127—791no—
1180#126—792no—
1181#126—792no—
1182#126—798no—
1183#126—798no—
1184#126—798no—
1185#126—798no—
1186#126—798no—
1187#126—798no—
1188#126—798no—
1189#126—798no—
1190#126—792no—
1191#126—792no—
1192#126—798no—
1193#126—798no—
1194#126—798no—
1195#126—798no—
1196#126—798no—
1197#126—798no—
1198#126C22×D7918yes—
1199#126C22×D7918yes—
1200#125—794no—
1201#125—794no—
1202#125—794no—
1203#125—792no—
1204#125—794no—
1205#125—792no—
1206#125—794no—
1207#125—794no—
1208#125—792no—
1209#125—791no—
1210#125—791no—
1211#125—792no—
1212#125—798no—
1213#125—794no—
1214#125—798no—
1215#125—798no—
1216#125—798no—
1217#125—798no—
1218#125—794no—
1219#125—794no—
1220#125—794no—
1221#125—798no—
1222#125—798no—
1223#125—798no—
1224#125—798no—
1225#125—798no—
1226#125—798no—
1227#125—798no—
1228#125—798no—
1229#125—798no—
1230#125—798no—
1231#125—798no—
1232#125—792no—
1233#125—794no—
1234#125—794no—
1235#125—798no—
1236#125—798no—
1237#125—798no—
1238#125C22×D7912yes—
1239#125C22×D7914yes—
1240#125C22×D7914yes—
1241#125C22×D7918yes—
1242#125C22×D7918yes—
1243#124—791no—
1244#124—794no—
1245#124—791no—
1246#124—792no—
1247#124—792no—
1248#124—798no—
1249#124—798no—
1250#124—798no—
1251#124C22×D7914yes—
1252#123—792no—
1253#123—798no—
1254#123—792no—
1255#123—792no—
1256#123—798no—
1257#123—798no—
1258#123—792no—
1259#123—792no—
1260#123—792no—
1261#123—798no—
1262#123—798no—
1263#123—798no—
1264#123—798no—
1265#123C22×D7918yes—
1266C22⋊Q8—794no—
1267C22⋊Q8—792no—
1268C22⋊Q8—794no—
1269C22⋊Q8—794no—
1270C22⋊Q8—794no—
1271C22⋊Q8—792no—
1272C22⋊Q8—791no—
1273C22⋊Q8—791no—
1274C22⋊Q8—794no—
1275C22⋊Q8—794no—
1276C22⋊Q8—794no—
1277C22⋊Q8—792no—
1278C22⋊Q8—792no—
1279C22⋊Q8—794no—
1280C22⋊Q8—794no—
1281C22⋊Q8—792no—
1282C22⋊Q8—794no—
1283C22⋊Q8—794no—
1284C22⋊Q8—794no—
1285C22⋊Q8—794no—
1286C22⋊Q8—792no—
1287C22⋊Q8—794no—
1288C22⋊Q8—794no—
1289C22⋊Q8—791no—
1290C22⋊Q8—792no—
1291C22⋊Q8—791no—
1292C22⋊Q8—792no—
1293C22⋊Q8—794no—
1294C22⋊Q8—794no—
1295C22⋊Q8—794no—
1296C22⋊Q8—798no—
1297C22⋊Q8—798no—
1298C22⋊Q8—798no—
1299C22⋊Q8—798no—
1300C22⋊Q8—798no—
1301C22⋊Q8—798no—
1302C22⋊Q8—794no—
1303C22⋊Q8—794no—
1304C22⋊Q8—792no—
1305C22⋊Q8—792no—
1306C22⋊Q8—798no—
1307C22⋊Q8—798no—
1308C22⋊Q8—798no—
1309C22⋊Q8—798no—
1310C22⋊Q8—798no—
1311C22⋊Q8—798no—
1312C22⋊Q8C22×D7912yes—
1313C22⋊Q8C22×D7912yes—
1314C22⋊Q8C22×D7914yes—
1315C22⋊Q8C22×D7914yes—
1316C22⋊Q8C22×D7914yes—
1317C22⋊Q8C22×D7914yes—
1318#121—791no—
1319#121—792no—
1320#121—792no—
1321#121—791no—
1322#121—791no—
1323#121—791no—
1324#121—792no—
1325#121—792no—
1326#120—792no—
1327#120—792no—
1328C4×Q8—792no—
1329C4×Q8—794no—
1330C4×Q8—792no—
1331C4×Q8—794no—
1332C4×Q8—794no—
1333C4×Q8—794no—
1334C4×Q8—794no—
1335C4×Q8—794no—
1336C4×Q8—794no—
1337C4×Q8—794no—
1338C4×Q8—794no—
1339C4×Q8—794no—
1340C4×Q8—792no—
1341C4×Q8—794no—
1342C4×Q8—794no—
1343C4×Q8—794no—
1344C4×Q8—794no—
1345C4×Q8—792no—
1346C4×Q8—794no—
1347C4×Q8—794no—
1348C4×Q8—798no—
1349C4×Q8—794no—
1350C4×Q8—794no—
1351C4×Q8—798no—
1352C4×Q8—794no—
1353C4×Q8—792no—
1354C4×Q8—792no—
1355C4×Q8—794no—
1356C4×Q8—794no—
1357C4×Q8—792no—
1358C4×Q8—792no—
1359C4×Q8—792no—
1360C4×Q8—791no—
1361C4×Q8—792no—
1362C4×Q8—791no—
1363C4×Q8—794no—
1364C4×Q8—794no—
1365C4×Q8—798no—
1366C4×Q8—798no—
1367C4×Q8—798no—
1368C4×Q8—798no—
1369C4×Q8—798no—
1370C4×Q8—794no—
1371C4×Q8C22×D7912yes—
1372C4×Q8C22×D7912yes—
1373C4×Q8C22×D7911yescharacteristic
1374C4×Q8C22×D7911yescharacteristic
1375C4×Q8C22×D7914yes—
1376C4×Q8C22×D7914yes—
1377C4×Q8C22×D7914yes—
1378C4×Q8C22×D7914yes—
1379C4×Q8C22×D7914yes—
1380C4×Q8C22×D7914yes—
1381C4×D4—798no—
1382C4×D4—794no—
1383C4×D4—792no—
1384C4×D4—792no—
1385C4×D4—792no—
1386C4×D4—792no—
1387C4×D4—792no—
1388C4×D4—792no—
1389C4×D4—792no—
1390C4×D4—792no—
1391C4×D4—792no—
1392C4×D4—792no—
1393C4×D4—798no—
1394C4×D4—798no—
1395C4×D4—798no—
1396C4×D4—792no—
1397C4×D4—792no—
1398C4×D4—792no—
1399C4×D4—792no—
1400C4×D4—791no—
1401C4×D4—791no—
1402C4×D4—798no—
1403C4×D4—794no—
1404C4×D4C22×D7912yes—
1405C4×D4C22×D7912yes—
1406C4×D4C22×D7911yescharacteristic
1407C4×D4C22×D7911yescharacteristic
1408#117—792no—
1409#117—791no—
1410#117—792no—
1411#117—792no—
1412#117—798no—
1413#117—794no—
1414#117—794no—
1415#117—794no—
1416#117—794no—
1417#117—792no—
1418#117—794no—
1419#117—792no—
1420#117—798no—
1421#117—794no—
1422#117—798no—
1423#117—794no—
1424#117—794no—
1425#117—794no—
1426#117—798no—
1427#117—798no—
1428#117—794no—
1429#117—792no—
1430#117—792no—
1431#117—792no—
1432#117—792no—
1433#117—792no—
1434#117—798no—
1435#117—798no—
1436#117C22×D7912yes—
1437#117C22×D7911yescharacteristic
1438#117C22×D7912yes—
1439#117C22×D7914yes—
1440#117C22×D7918yes—
1441#117C22×D7914yes—
1442C2×C4⋊C4—792no—
1443C2×C4⋊C4—792no—
1444C2×C4⋊C4—794no—
1445C2×C4⋊C4—794no—
1446C2×C4⋊C4—794no—
1447C2×C4⋊C4—794no—
1448C2×C4⋊C4—792no—
1449C2×C4⋊C4—792no—
1450C2×C4⋊C4—792no—
1451C2×C4⋊C4—794no—
1452C2×C4⋊C4—794no—
1453C2×C4⋊C4—792no—
1454C2×C4⋊C4—794no—
1455C2×C4⋊C4—794no—
1456C2×C4⋊C4C22×D7912yes—
1457C2×C4⋊C4C22×D7912yes—
1458C2×C22⋊C4—794no—
1459C2×C22⋊C4—794no—
1460C2×C42—794no—
1461C2×C42—791no—
1462C2×C42—791no—
1463C2×C42—791no—
1464C2×C42—794no—
1465C2×C42—791no—
1466C2×C42—791no—
1467C2×C42—792no—
1468C2×C42—791no—
1469C2×C42—791no—
1470C2×C42—791no—
1471C2×C42—791no—
1472C2×C42—791no—
1473C2×C42—791no—
1474C2×C42C22×D7912yes—
1475C2×C42C22×D7911yescharacteristic
1476C24—791no—
1477#41—24no—
1478#41—3164no—
1479#41—1588no—
1480#41—1584no—
1481C2×Q8—28no—
1482C2×Q8—3164no—
1483C2×Q8—3168no—
1484C2×Q8—3164no—
1485C2×Q8—3168no—
1486C2×Q8—794no—
1487C2×Q8—794no—
1488C2×Q8—798no—
1489C2×Q8—798no—
1490C2×Q8—792no—
1491C2×Q8—792no—
1492C2×Q8—794no—
1493C2×Q8—792no—
1494C2×Q8—791no—
1495C2×Q8—794no—
1496C2×Q8—792no—
1497C2×Q8—1588no—
1498C2×Q8C23×D7914yes—
1499C2×Q8C23×D7914yes—
1500C2×Q8C23×D7911yescharacteristic
1501C2×Q8C23×D7912yes—
1502C2×Q8C23×D7912yes—
1503C2×D4—792no—
1504C2×D4—792no—
1505C2×D4—792no—
1506C2×D4—792no—
1507C2×D4—792no—
1508C2×D4—792no—
1509C2×D4—792no—
1510C2×D4—791no—
1511C2×D4C23×D7912yes—
1512C2×D4C23×D7911yescharacteristic
1513C22×C4—3162no—
1514C22×C4—791no—
1515C22×C4—794no—
1516C22×C4—798no—
1517C22×C4—791no—
1518C22×C4—791no—
1519C22×C4—794no—
1520C22×C4—798no—
1521C22×C4—791no—
1522C22×C4—791no—
1523C22×C4—791no—
1524C22×C4—791no—
1525C22×C4—791no—
1526C22×C4—791no—
1527C22×C4—791no—
1528C22×C4—791no—
1529C22×C4—791no—
1530C22×C4—791no—
1531C22×C4—791no—
1532C22×C4—791no—
1533C22×C4—794no—
1534C22×C4—792no—
1535C22×C4—792no—
1536C22×C4—792no—
1537C22×C4—1584no—
1538C22×C4—1584no—
1539C22×C4C23×D7911yescharacteristic
1540C22×C4C23×D7911yescharacteristic
1541C22×C4C23×D7914yes—
1542C22×C4C23×D7912yes—
1543C22×C4C23×D7912yes—
1544C22×C4C23×D7912yes—
1545C22×C4C23×D7911yescharacteristic
1546C4⋊C4—798no—
1547C4⋊C4—794no—
1548C4⋊C4—794no—
1549C4⋊C4—794no—
1550C4⋊C4—794no—
1551C4⋊C4—798no—
1552C4⋊C4—798no—
1553C4⋊C4—794no—
1554C4⋊C4—798no—
1555C4⋊C4—794no—
1556C4⋊C4—794no—
1557C4⋊C4—794no—
1558C4⋊C4—792no—
1559C4⋊C4—792no—
1560C4⋊C4—792no—
1561C4⋊C4—792no—
1562C4⋊C4—792no—
1563C4⋊C4—792no—
1564C4⋊C4—792no—
1565C4⋊C4—792no—
1566C4⋊C4—792no—
1567C4⋊C4—792no—
1568C4⋊C4—798no—
1569C4⋊C4—798no—
1570C4⋊C4—798no—
1571C4⋊C4—798no—
1572C4⋊C4—798no—
1573C4⋊C4—794no—
1574C4⋊C4—792no—
1575C4⋊C4—794no—
1576C4⋊C4—792no—
1577C4⋊C4—792no—
1578C4⋊C4—792no—
1579C4⋊C4—794no—
1580C4⋊C4—794no—
1581C4⋊C4—794no—
1582C4⋊C4—798no—
1583C4⋊C4—798no—
1584C4⋊C4—798no—
1585C4⋊C4—798no—
1586C4⋊C4—794no—
1587C4⋊C4—791no—
1588C4⋊C4—791no—
1589C4⋊C4—792no—
1590C4⋊C4—792no—
1591C4⋊C4—792no—
1592C4⋊C4—792no—
1593C4⋊C4—798no—
1594C4⋊C4—798no—
1595C4⋊C4—798no—
1596C4⋊C4C23×D7912yes—
1597C4⋊C4C23×D7912yes—
1598C4⋊C4C23×D7912yes—
1599C4⋊C4C23×D7912yes—
1600C4⋊C4C23×D7914yes—
1601C4⋊C4C23×D7914yes—
1602C4⋊C4C23×D7914yes—
1603C4⋊C4C23×D7914yes—
1604C4⋊C4C23×D7914yes—
1605C4⋊C4C23×D7914yes—
1606C4⋊C4C23×D7918yes—
1607C4⋊C4C23×D7918yes—
1608C4⋊C4C23×D7911yescharacteristic
1609C4⋊C4C23×D7911yescharacteristic
1610C4⋊C4C23×D7912yes—
1611C4⋊C4C23×D7912yes—
1612C4⋊C4C23×D7918yes—
1613C4⋊C4C23×D7918yes—
1614C22⋊C4—794no—
1615C22⋊C4—792no—
1616C22⋊C4—792no—
1617C22⋊C4—792no—
1618C22⋊C4—792no—
1619C22⋊C4—792no—
1620C22⋊C4—798no—
1621C22⋊C4—798no—
1622C22⋊C4—794no—
1623C22⋊C4—798no—
1624C22⋊C4—794no—
1625C22⋊C4—792no—
1626C22⋊C4—792no—
1627C22⋊C4—792no—
1628C22⋊C4—792no—
1629C22⋊C4—798no—
1630C22⋊C4—792no—
1631C22⋊C4—792no—
1632C22⋊C4—792no—
1633C22⋊C4—792no—
1634C22⋊C4—792no—
1635C22⋊C4—792no—
1636C22⋊C4—798no—
1637C22⋊C4—798no—
1638C22⋊C4C23×D7914yes—
1639C22⋊C4C23×D7918yes—
1640C22⋊C4C23×D7912yes—
1641C22⋊C4C23×D7918yes—
1642C22⋊C4C23×D7912yes—
1643C22⋊C4C23×D7912yes—
1644C42—791no—
1645C42—791no—
1646C42—791no—
1647C42—791no—
1648C42—791no—
1649C42—791no—
1650C42—791no—
1651C42—791no—
1652C42—791no—
1653C42—791no—
1654C42—791no—
1655C42—791no—
1656C42—794no—
1657C42—798no—
1658C42—794no—
1659C42—792no—
1660C42—792no—
1661C42—792no—
1662C42—798no—
1663C42—794no—
1664C42—798no—
1665C42—798no—
1666C42—798no—
1667C42—798no—
1668C42C23×D7911yescharacteristic
1669C42C23×D7911yescharacteristic
1670C42C23×D7911yescharacteristic
1671C42C23×D7911yescharacteristic
1672C42C23×D7914yes—
1673C42C23×D7912yes—
1674C42C23×D7912yes—
1675C42C23×D7912yes—
1676C42C23×D7918yes—
1677C42C23×D7918yes—
1678C23—3161no—
1679C23—791no—
1680C23—791no—
1681C23—792no—
1682C23—1582no—
1683C23—1582no—
1684C23C24×D7912yes—
1685C23C24×D7911yescharacteristic
1686Q8—24no—
1687Q8—28no—
1688Q8—28no—
1689Q8—22no—
1690Q8—24no—
1691Q8—3164no—
1692Q8—3168no—
1693Q8—3164no—
1694Q8—3168no—
1695Q8—3162no—
1696Q8—1588no—
1697Q8—1584no—
1698Q8—1584no—
1699Q8—1582no—
1700Q8—1588no—
1701Q8—1584no—
1702D4—24no—
1703D4—22no—
1704D4—3162no—
1705D4—3162no—
1706D4—3162no—
1707D4—1584no—
1708D4—1584no—
1709D4—1584no—
1710D4—1584no—
1711D4—1582no—
1712C2×C4—28no—
1713C2×C4—22no—
1714C2×C4—24no—
1715C2×C4—24no—
1716C2×C4—22no—
1717C2×C4—24no—
1718C2×C4—3161no—
1719C2×C4—3161no—
1720C2×C4—3168no—
1721C2×C4—3164no—
1722C2×C4—3161no—
1723C2×C4—3164no—
1724C2×C4—3168no—
1725C2×C4—791no—
1726C2×C4—794no—
1727C2×C4—791no—
1728C2×C4—791no—
1729C2×C4—794no—
1730C2×C4—792no—
1731C2×C4—792no—
1732C2×C4—792no—
1733C2×C4—791no—
1734C2×C4—794no—
1735C2×C4—798no—
1736C2×C4—791no—
1737C2×C4—791no—
1738C2×C4—1582no—
1739C2×C4—1582no—
1740C2×C4—1588no—
1741C2×C4—1582no—
1742C2×C4—1582no—
1743C2×C4—1582no—
1744C2×C4—1584no—
1745C2×C4—1582no—
1746C2×C4—1582no—
1747C2×C4—1582no—
1748C2×C4—1582no—
1749C2×C4—1584no—
1750C2×C4—1582no—
1751C2×C4—1582no—
1752C2×C4—1584no—
1753C2×C4#1457920814yes—
1754C2×C4C24×D7918yes—
1755C2×C4C24×D7912yes—
1756C2×C4C24×D7914yes—
1757C2×C4C24×D7911yescharacteristic
1758C2×C4C24×D7911yescharacteristic
1759C2×C4C24×D7914yes—
1760C2×C4C24×D7912yes—
1761C2×C4C24×D7912yes—
1762C2×C4C24×D7911yescharacteristic
1763C2×C4C24×D7911yescharacteristic
1764C2×C4C24×D7911yescharacteristic
1765C2×C4C24×D7911yescharacteristic
1766C22—21no—
1767C22—21no—
1768C22—22no—
1769C22—22no—
1770C22—22no—
1771C22—3164no—
1772C22—792no—
1773C22—1581no—
1774C22—1582no—
1775C22—1581no—
1776C22—1582no—
1777C22—1582no—
1778C22—1581no—
1779C22—1581no—
1780C22—1581no—
1781C22C2×#1457920812yes—
1782C22C25×D7911yescharacteristic
1783C4—21no—
1784C4—22no—
1785C4—24no—
1786C4—22no—
1787C4—28no—
1788C4—21no—
1789C4—22no—
1790C4—24no—
1791C4—792no—
1792C4—1581no—
1793C4—1582no—
1794C4—1584no—
1795C4—1581no—
1796C4—1581no—
1797C4—1582no—
1798C4—1588no—
1799C4—1584no—
1800C4—1581no—
1801C4—1581no—
1802C4—1582no—
1803C42−1+4×D7912yes—
1804C4C2×#1457920812yes—
1805C4C2×#1457920812yes—
1806C4#1909940012yes—
1807C2—22no—
1808C2—42no—
1809C2—3161no—
1810C2—3162no—
1811C2—1582no—
1812C2C2×2−1+4×D7911yescharacteristic
1813C2C22×#1457920811yescharacteristic
1814C2C2×#1909940011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3509C2
prime radical#23776693C2
hypercenter#3509D79
hypocenterC79#62837
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3509

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23778005C2semidirect
2. #23778001C2semidirect
3. #23777892C2semidirect
4. #23777884C2semidirect
5. #23777877C2semidirect
6. #23777876C2semidirect
7. #23777813C2semidirect
8. #23777646C2semidirect
9. #23777497C2semidirect
10. #23777495C2semidirect
11. #23777489C2semidirect
12. #23777287C2semidirect
13. #23777284C2semidirect
14. #23777279C2semidirect
15. #23777279C2semidirect
16. #23777264C2semidirect
17. #23777255C2semidirect
18. #23777219C2semidirect
19. #23777212C2semidirect
20. #23777212C2semidirect
21. #23777206C2semidirect
22. #23777204C2semidirect
23. #23777149C2semidirect
24. #23777142C2semidirect
25. #23777141C2semidirect
27. C2×#19099118C2semidirect
28. #533×D79C2semidirect
29. C79×#3509C2semidirect
30. C79⋊#564C22semidirect
33. #19099315C22semidirect
34. #19099295C22semidirect
35. Q8×Dic158C22semidirect
36. Q8×Dic158C22semidirect
37. Q8×Dic158C22semidirect
38. Q8×Dic158C22semidirect
39. #19099292C22semidirect
40. #19099292C22semidirect
41. #19099292C22semidirect
42. #19099292C22semidirect
43. #19099291C22semidirect
44. #19099291C22semidirect
45. #19099290C22semidirect
46. #19099290C22semidirect
47. #19099290C22semidirect
48. #19099289C22semidirect
49. #19099289C22semidirect
50. #19099289C22semidirect
51. #19099289C22semidirect
52. #19099288C22semidirect
53. #19099288C22semidirect
54. #19099288C22semidirect
55. #19099287C22semidirect
56. #19099287C22semidirect
57. #19099287C22semidirect
61. #19099284C22semidirect
62. #19099282C22semidirect
64. #19099281C22semidirect
65. #19099280C22semidirect
67. #19099273C22semidirect
70. #19099271C22semidirect
72. #19099270C22semidirect
75. #19099255C22semidirect
76. #19099255C22semidirect
80. #19099252C22semidirect
89. #19099247C22semidirect
94. Q8×D316C22semidirect
96. D4×Dic158C22semidirect
99. #19099226C22semidirect
102. #19099193C22semidirect
103. #19099193C22semidirect
107. #19099191C22semidirect
108. #19099191C22semidirect
113. #19099176C22semidirect
114. #19099176C22semidirect
116. #19099174C22semidirect
117. #19099173C22semidirect
118. #19099173C22semidirect
120. #19099172C22semidirect
123. #19099171C22semidirect
124. #19099170C22semidirect
125. #19099170C22semidirect
133. #19099120C22semidirect
146. #19099118C22semidirect
147. #19099118C22semidirect
148. #19099118C22semidirect
163. C2×#14579161C22semidirect
166. C4⋊Q8×D79C22semidirect
192. #19099040C22semidirect
194. #19099039C22semidirect
205. #557×C79C22semidirect
206. #557×C79C22semidirect
207. #556×C79C22semidirect
208. #556×C79C22semidirect
211. #541×C79C22semidirect
214. #533×C79C22semidirect
215. #533×C79C22semidirect
923. #3509D79semidirect
937. C79#62837semidirect
963. #557C2×D79semidirect
964. #557C2×D79semidirect
976. #556C2×D79semidirect
977. #556C2×D79semidirect
1040. #541C2×D79semidirect
1076. #533C2×D79semidirect
1077. #533C2×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237780052
#237780012
#237778922
#237778842
#237778772
#237778762
#237778132
#237776462
#237774972
#237774952
#237774892
#237772872
#237772842
#237772792
#237772642
#237772552
#237772192
#237772122
#237772062
#237772042
#237771492
#237771422
#237771412
#237766932
C2×#190991182
#533×D792
C79×#35092
#6283779